### Nuprl Lemma : two-implies-quotient-true

`∀[P,Q,R:ℙ].  ((P `` Q `` R) `` {⇃(P) `` ⇃(Q) `` ⇃(R)})`

Proof

Definitions occuring in Statement :  quotient: `x,y:A//B[x; y]` uall: `∀[x:A]. B[x]` prop: `ℙ` guard: `{T}` implies: `P `` Q` true: `True`
Definitions unfolded in proof :  guard: `{T}` uall: `∀[x:A]. B[x]` implies: `P `` Q` member: `t ∈ T` prop: `ℙ` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` uimplies: `b supposing a` quotient: `x,y:A//B[x; y]` and: `P ∧ Q` all: `∀x:A. B[x]` subtype_rel: `A ⊆r B` true: `True`
Lemmas referenced :  quotient_wf true_wf equiv_rel_true quotient-member-eq equal-wf-base
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation rename introduction pointwiseFunctionalityForEquality cut lemma_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality lambdaEquality hypothesis because_Cache independent_isectElimination pertypeElimination productElimination dependent_functionElimination applyEquality functionEquality independent_functionElimination natural_numberEquality productEquality universeEquality

Latex:
\mforall{}[P,Q,R:\mBbbP{}].    ((P  {}\mRightarrow{}  Q  {}\mRightarrow{}  R)  {}\mRightarrow{}  \{\00D9(P)  {}\mRightarrow{}  \00D9(Q)  {}\mRightarrow{}  \00D9(R)\})

Date html generated: 2016_05_14-AM-06_08_51
Last ObjectModification: 2015_12_26-AM-11_48_23

Theory : quot_1

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